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Reduced-order models were derived for plane Couette flow using Galerkin projection, with orthonormal basis functions taken as the leading controllability modes of the linearised Navier-Stokes system for a few low wavenumbers. Resulting…

Fluid Dynamics · Physics 2022-07-15 André V. G. Cavalieri , Petrônio A. S. Nogueira

In this paper, we analyze a hybridized discontinuous Galerkin(HDG) method with reduced stabilization for the Stokes equations. The reduced stabilization enables us to reduce the number of facet unknowns and improve the computational…

Numerical Analysis · Mathematics 2015-08-12 Issei Oikawa

We consider discontinuous Galerkin methods for an elliptic distributed optimal control problem constrained by a convection-dominated problem. We prove global optimal convergence rates using an inf-sup condition, with the diffusion parameter…

Numerical Analysis · Mathematics 2024-06-14 Sijing Liu , Valeria Simoncini

This paper deals with time-optimal control of nonlinear continuous-time systems based on direct collocation. The underlying discretization grid is variable in time, as the time intervals are subject to optimization. This technique differs…

Systems and Control · Electrical Eng. & Systems 2020-05-26 Christoph Rösmann , Artemi Makarow , Torsten Bertram

Distributed-order PDEs are tractable mathematical models for complex multiscaling anomalous transport, where derivative orders are distributed over a range of values. We develop a fast and stable Petrov-Galerkin spectral method for such…

Numerical Analysis · Mathematics 2018-05-23 Mehdi Samiee , Ehsan Kharazmi , Mohsen Zayernouri , Mark M Meerschaert

We consider a second-order linear system of ordinary differential equations (ODEs) including random variables. A stochastic Galerkin method yields a larger deterministic linear system of ODEs. We apply a model order reduction (MOR) of this…

Numerical Analysis · Mathematics 2023-07-11 Roland Pulch

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when…

Fluid Dynamics · Physics 2021-12-15 Shady E. Ahmed , Omer San , Adil Rasheed , Traian Iliescu

We consider variational discretization of a parabolic optimal control problem governed by space-time measure controls. For the state discretization we use a Petrov-Galerkin method employing piecewise constant states and piecewise linear and…

Optimization and Control · Mathematics 2019-11-25 Evelyn Herberg , Michael Hinze , Henrik Schumacher

We consider fully discrete finite element approximations for a semilinear optimal control system of partial differential equations in two cases: for distributed and Robin boundary control. The ecological predator-prey optimal control model…

Numerical Analysis · Mathematics 2024-04-25 EFthymios N. Karatzas

This paper introduces a reduced-order modeling approach based on finite volume methods for hyperbolic systems, combining Proper Orthogonal Decomposition (POD) with the Discrete Empirical Interpolation Method (DEIM) and Proper Interval…

Numerical Analysis · Mathematics 2025-05-07 I. Gómez-Bueno , E. D. Fernández-Nieto , S. Rubino

In this work, the space-time MORe DWR (Model Order Reduction with Dual-Weighted Residual error estimates) framework is extended and further developed for single-phase flow problems in porous media. Specifically, our problem statement is the…

Numerical Analysis · Mathematics 2023-11-16 Hendrik Fischer , Julian Roth , Ludovic Chamoin , Amelie Fau , Mary F. Wheeler , Thomas Wick

This paper is devoted to the numerical analysis of a control constrained distributed optimal control problem subject to a time fractional diffusion equation with non-smooth initial data. The solutions of state and co-state are decomposed…

Numerical Analysis · Mathematics 2020-10-06 Tao Wang , Binjie Li , Xiaoping Xie

In this paper we consider a reduced order method for the approximation of the eigensolutions of the Laplace problem with Dirichlet boundary condition. We use a time continuation technique that consists in the introduction of a fictitious…

Numerical Analysis · Mathematics 2022-12-14 Fleurianne Bertrand , Daniele Boffi , Abdul Halim

This paper deals with a stochastic optimal feedback control problem for the controlled stochastic partial differential equations. More precisely, we establish the existence of stochastic optimal feedback control for the controlled…

Probability · Mathematics 2025-01-07 Gaofeng Zong

We introduce in this paper a technique for the reduced order approximation of parametric symmetric elliptic partial differential equations. For any given dimension, we prove the existence of an optimal subspace of at most that dimension…

Analysis of PDEs · Mathematics 2017-07-06 M. Azaïez , F. Ben Belgacem , J. Casado-Díaz , T. Chacón Rebollo , F. Murat

We propose a goal-oriented mesh-adaptive algorithm for a finite element method stabilized via residual minimization on dual discontinuous-Galerkin norms. By solving a saddle-point problem, this residual minimization delivers a stable…

Numerical Analysis · Mathematics 2021-02-24 Sergio Rojas , David Pardo , Pouria Behnoudfar , Victor M. Calo

Genetic Algorithm (GA) has been used in this paper for a new Nyquist based sub-optimal model reduction and optimal time domain tuning of PID and fractional order (FO) PI{\lambda}D{\mu} controllers. Comparative studies show that the new…

Systems and Control · Computer Science 2012-02-28 Saptarshi Das , Indranil Pan , Shantanu Das , Amitava Gupta

This work addresses optimal control problems governed by a linear time-dependent partial differential equation (PDE) as well as integer constraints on the control. Moreover, partial observations are assumed in the objective function. The…

Optimization and Control · Mathematics 2021-10-08 Dominik Garmatter , Margherita Porcelli , Francesco Rinaldi , Martin Stoll

In this paper, we propose an a-priori error estimate for the model order reduction (MOR) method of space-time proper orthogonal decomposition (space-time POD). The original space-time POD approach extends standard POD by reducing not only…

Numerical Analysis · Mathematics 2026-04-27 Carmen Gräßle , Jan Heiland , Jannis Marquardt

In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems efficiently. Our method consists of offline and online stages. In the off-line stage, we explore the low-dimensional structures in the…

Numerical Analysis · Mathematics 2021-10-18 Zhongjian Wang , Wenlong Zhang , Zhiwen Zhang